Finding position-to-term rules

Find position-to-term rules for these sequences:

Squares investigation

Imagine a 3 x 3 square:

Squares investigation Imagine a 3 x 3 square: Colour the outside red:

Squares investigation Imagine a 3 x 3 square: Colour the outside red:

Squares investigation How many of the small squares have  0 red sides?  1 red side?  2 red sides?  3 red sides?  4 red sides?

Squares investigation Now change the size of the starting square to 2 x 2 ? 4 x 4 ? etc…

Squares investigation How many of the small squares now have  0 red sides?  1 red side?  2 red sides?  3 red sides?  4 red sides? INVESTIGATE!

Generalising from Diagrams 8 by 8

Generalising from Diagrams 20 by by by 100 n by n 2 red sides = ? 1 red side = ? 0 red sides = ?

Generalising from Diagram 20 by by by 50 a by b 2 red sides = ? 1 red side = ? 0 red sides = ?

Squares investigation Put your results into a table! (If you need to) Work methodically! Spot patterns! Try to find some general rules!